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Homogenization of
nonlinear inextensible pantographic structures by
$\Gamma$-convergence
Jean-Jacques Alibert and Alessandro Della Corte
Vol. 7 (2019), No. 1, 1–24
DOI: 10.2140/memocs.2019.7.1
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Abstract |
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We prove the -convergence of a pantographic microstructured sheet with inextensible fibers to a 2D generalized continuum model. Large deformations considered as geometrical nonlinearities are taken into account, and the -convergence argument is developed in terms of convergence of measure functionals. We also prove a relative compactness property for the sequence of discrete energy functionals. |
Keywords
$\Gamma$-convergence, nonlinear elasticity, generalized
continua, pantographic structures
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Mathematical Subject Classification 2010
Primary: 46G10, 74B20, 74Q05
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Milestones
Received: 4 April 2018
Revised: 1 October 2018
Accepted: 29 November 2018
Published: 22 April 2019
Communicated by Pierre Seppecher
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Authors |
| Jean-Jacques Alibert | |
| Institut de Mathématiques de
Toulon Université de Toulon La Garde France |
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| Alessandro Della Corte | |
| International Research Center for
the Mathematics and Mechanics of Complex Systems Università degli Studi dell’Aquila L’Aquila Italy |
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